Shipping is always a viable option but depending on where you're going it may be overkill in my opinion. I travel to Chicago from Pittsburgh with all of my gear without shipping it and have not once had a problem. This has been an annual pilgrimage the past 4 years, in fact my last experiences traveling to/from were within the past 3 weeks. I use a duffel to store my boots, waders, and flies, clothes and that bag gets checked. I keep my reels in a backpack and carry them on, they're tucked under the seat. Rods go in a nylon faced multi rod tube and are carried on, stored in overhead storage. These are all 4 piece rods in a 4 piece tube.

No issues on Southwest. Its worthwhile to check your carrier and even the size of your plane as some seem to have different rules than others and could be limited to space.

Some options for rod tubes:

If the quality of this is anything like the Maine Guide Reel cases, it should be excellent. You could put your two metal tubes inside this one.